ABSTRACT In this paper, we consider general scalar robust optimization problems and study the characterizations for optimality conditions in the general vector spaces where we do not require any topology on the considered space. By using the image space analysis and nonlinear separation function, we derive some necessary and sufficient optimality conditions, especially saddle point sufficient optimality conditions for scalar robust optimization problems. Moreover, we discuss the validity and effectiveness of our results for the shortest path problem.

中文翻译：

---

通过图像空间分析表征鲁棒优化条件

摘要在本文中，我们考虑了一般标量鲁棒优化问题，并研究了一般向量空间中最优条件的表征，其中我们不需要考虑空间上的任何拓扑。利用图像空间分析和非线性分离函数，推导出了一些充分必要的最优条件，尤其是标量鲁棒优化问题的鞍点充分最优条件。此外，我们讨论了我们的结果对最短路径问题的有效性和有效性。